One of the requirements for a celestial object to be a planet is that the object must have "cleared the neighbourhood around its orbit". There are thousands of asteroids come near Earth, and near the other inner planets. Doesn't that mean that the inner planets have not cleared their neighborhood? How can they be considered planets?

The asteroids that come into the inner solar system (near Earth) are much less massive than any planet, so Mercury, Venus, Earth, and Mars do not get demoted because of asteroids (or comets). Mercury is the smallest and least massive planet in our solar system, and the estimated total mass of the asteroids is less than 1% of the mass of Mercury. There are lots of small objects that are waiting to be discovered, but we have enough observations to say that there cannot be any other bodies in the inner solar system that are large enough to be considered planets.

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